ACCELERATOR PHYSICS AND RELATIVISTIC ELECTRODYNAMICS
Course objectives
ENG GENERAL The course aims to provide students with an understanding of the principles of special relativity with a focus on the application to particle accelerator physics. The connection between relativity and classical mechanics, electromagnetism and the transformation of fields between inertial reference frames will be discussed. The course will also introduce the fundamentals of relativistic motion of charges in electric and magnetic fields, with a focus on the operation of modern particle accelerators, including linear accelerators, cyclotrons and synchrotrons. The final goal is to provide students not only with the theoretical knowledge but also with the practical skills needed to analyze and design particle acceleration schemes and related devices. Through the study of betatron and synchrotron motion, students will be able to understand the operation of circular accelerators and to use simulation tools such as the XSuite code (https://xsuite.readthedocs.io/en/latest/) independently. SPECIFIC • Knowledge and understanding: to acquire knowledge of the principles of special relativity and their application to the physics of particle accelerators, including the transformations of electromagnetic fields between inertial systems and the operation of linear and circular accelerators. • Applying knowledge and understanding: to analyze the motion of charges in different devices such as magnetic dipoles and quadrupoles, as well as evaluate the power radiated by electric charges in circular accelerators. • Making judgements: to develop the ability to evaluate the operation of circular accelerators through the study of the motion of betatrons and synchrotrons and to independently use the XSuite code for the simulation of beam dynamics. • Communication skills: explain clearly and rigorously, the concepts related to particle accelerators, using the appropriate technical language. • Learning skills: to develop skills that will allow a student to independently study advanced topics in the field of accelerator physics and related technologies.
Channel 1
MAURO MIGLIORATI
Lecturers' profile
Program - Frequency - Exams
Course program
Review of the fundamental laws of classical physics.
Galileo's principle of relativity, Newtonian mechanics. Galilean transformations, absolute space and time. Maxwell's equations. Electromagnetic waves.
Limits of classical mechanics and special relativity theory.
Ether theory. Michelson and Morley experiment, alternative theories to explain the results. Lorentz transformations and relativistic kinematics. Concept of simultaneity, time dilation, length contraction. Transformation of velocities, relativistic dynamics, momentum, energy, transformation of forces.
Maxwell's equations and Relativity.
Transformations of charge and current densities, transformation of E and B fields and potentials. Field of a charge in uniform rectilinear motion. Covariance of Maxwell's equations.
Relativistic electrodynamics and applications to particle accelerators.
Equations of motion of a charge in an electromagnetic field in Cartesian and cylindrical coordinates. Accelerated charge in an electric field. Bending effects of the B field, cyclotron motion. Multipolar development of the magnetic field in magnetic devices for accelerators.
Longitudinal and transverse dynamics of a particle beam. Synchrotron radiation. Accelerator technologies and systems. Radiofrequency accelerating systems. Focusing and bending systems in particle accelerators. Linear accelerators. Circular accelerators. Stability and control of particle beams.
Prerequisites
The student must have basic knowledge of mechanics and electromagnetism
No prerequisites are requested.
Books
Notes distributed by the professor
Textbooks specialized in particle accelerators, such as: S. Y. Lee, Accelerator Physics, World Scientific.
Teaching mode
Lectures with exercises and numerical examples.
In the event that, due to the pandemic emergency, it is not possible to carry out lessons in person, the course modality will be of the blended or remote type depending on the regulatory provisions.
Frequency
Attendance at the course is optional
Exam mode
The written exam consists in exercises on relativity and radiation of an accelerated charge.
The oral exam consists in a report/presentation of the student of one of the topics of the course with in-depth analysis and questions concerning other arguments
Bibliography
S. Y. Lee, Accelerator Physics, World Scientific.
R. Resnick, Introduction to Special Relativity, John Wiley & Sons Inc.
Lesson mode
Explanation of the theory lessons and carrying out of exercises that follow the course program on a classic blackboard, interactive white board, tablet with projection in the classroom, or through presentations.
MAURO MIGLIORATI
Lecturers' profile
Program - Frequency - Exams
Course program
Review of the fundamental laws of classical physics.
Galileo's principle of relativity, Newtonian mechanics. Galilean transformations, absolute space and time. Maxwell's equations. Electromagnetic waves.
Limits of classical mechanics and special relativity theory.
Ether theory. Michelson and Morley experiment, alternative theories to explain the results. Lorentz transformations and relativistic kinematics. Concept of simultaneity, time dilation, length contraction. Transformation of velocities, relativistic dynamics, momentum, energy, transformation of forces.
Maxwell's equations and Relativity.
Transformations of charge and current densities, transformation of E and B fields and potentials. Field of a charge in uniform rectilinear motion. Covariance of Maxwell's equations.
Relativistic electrodynamics and applications to particle accelerators.
Equations of motion of a charge in an electromagnetic field in Cartesian and cylindrical coordinates. Accelerated charge in an electric field. Bending effects of the B field, cyclotron motion. Multipolar development of the magnetic field in magnetic devices for accelerators.
Longitudinal and transverse dynamics of a particle beam. Synchrotron radiation. Accelerator technologies and systems. Radiofrequency accelerating systems. Focusing and bending systems in particle accelerators. Linear accelerators. Circular accelerators. Stability and control of particle beams.
Prerequisites
The student must have basic knowledge of mechanics and electromagnetism
No prerequisites are requested.
Books
Notes distributed by the professor
Textbooks specialized in particle accelerators, such as: S. Y. Lee, Accelerator Physics, World Scientific.
Teaching mode
Lectures with exercises and numerical examples.
In the event that, due to the pandemic emergency, it is not possible to carry out lessons in person, the course modality will be of the blended or remote type depending on the regulatory provisions.
Frequency
Attendance at the course is optional
Exam mode
The written exam consists in exercises on relativity and radiation of an accelerated charge.
The oral exam consists in a report/presentation of the student of one of the topics of the course with in-depth analysis and questions concerning other arguments
Bibliography
S. Y. Lee, Accelerator Physics, World Scientific.
R. Resnick, Introduction to Special Relativity, John Wiley & Sons Inc.
Lesson mode
Explanation of the theory lessons and carrying out of exercises that follow the course program on a classic blackboard, interactive white board, tablet with projection in the classroom, or through presentations.
ANDREA MOSTACCI
Lecturers' profile
Program - Frequency - Exams
Course program
FIRST PART: Relativistic Electrodynamics.
1- Principles of classical mechanics and electromagnetism
Introduction, the principles of classical mechanics, the concept of absolute space and time, the Maxwell equations and the electromagnetic waves, the experiment of Michelson-Morley, the concept of ether.
2- Relativistic kinematics
The Lorentz transformations, introduction to space-time, concept of simultaneity and proper time, relativistic invariant, Minkowski space, relativistic Doppler effect.
3- Relativistic dynamics
Momentum, work and kinetic energy, equivalence of mass and energy, transformations of momentum and energy, pulse-energy quadrivector, transformations of forces.
4- Relativity and electromagnetism
Transformations of charge and current density, the covariance concept and the transformations of fields, potential quadrivector, e.m. field of a relativistic point charge with constant velocity, retarded potentials.
5- Relativistic electrodynamics
Brief review of analytical mechanics, the principle of virtual work, Lagrange equations, the Hamilton function, relativistic Hamiltonian of a charged particle.
SECOND PART: Accelerator Physics.
1- Introduction to particle accelerators
A brief history on particle accelerators, electrostatic accelerators, accelerators based on time varying fields, Cyclotrons, Betatrons and Linacs.
2- Beam dynamics
Phase stability in synchrotrons, field index and weak focusing, strong focusing colliders and storage rings.
3- Accelerator devices and new acceleration techniques
Dipoles, quadrupoles and sextupoles, RF cavities.
4- Transverse beam dynamics in circular accelerators
Hamiltonian in Fernet-Serret coordinate system, Hill’s equation, transverse beam dynamics, matrix formalism, betatron function and tune, Courant-Snyder invariant and Twiss parameters.
5- Longitudinal beam dynamics in circular accelerators
Electromagnetic fields in RF devices, standing wave and travelling wave structures, momentum compaction, slippage factor and transition energy, synchrotron oscillations with small and large amplitude.
Prerequisites
Basic Physics and Basic electromagnetism courses
Books
Notes from the teacher
Material available on the web site
https://classroom.google.com/c/MTc3OTM0NDMxOTg0
Teaching mode
Lectures and visits
Frequency
Attendance is optional, but recommended. If a student has not been able to carry out laboratory experiments for some reason, recovery days are to be arranged with the teacher.
Exam mode
The final exam is oral and includes the defence of review of topics studied in the course.
Lesson mode
The course is based on traditional lectures in class, with some visits of didactic interest.
ANDREA MOSTACCI
Lecturers' profile
Program - Frequency - Exams
Course program
FIRST PART: Relativistic Electrodynamics.
1- Principles of classical mechanics and electromagnetism
Introduction, the principles of classical mechanics, the concept of absolute space and time, the Maxwell equations and the electromagnetic waves, the experiment of Michelson-Morley, the concept of ether.
2- Relativistic kinematics
The Lorentz transformations, introduction to space-time, concept of simultaneity and proper time, relativistic invariant, Minkowski space, relativistic Doppler effect.
3- Relativistic dynamics
Momentum, work and kinetic energy, equivalence of mass and energy, transformations of momentum and energy, pulse-energy quadrivector, transformations of forces.
4- Relativity and electromagnetism
Transformations of charge and current density, the covariance concept and the transformations of fields, potential quadrivector, e.m. field of a relativistic point charge with constant velocity, retarded potentials.
5- Relativistic electrodynamics
Brief review of analytical mechanics, the principle of virtual work, Lagrange equations, the Hamilton function, relativistic Hamiltonian of a charged particle.
SECOND PART: Accelerator Physics.
1- Introduction to particle accelerators
A brief history on particle accelerators, electrostatic accelerators, accelerators based on time varying fields, Cyclotrons, Betatrons and Linacs.
2- Beam dynamics
Phase stability in synchrotrons, field index and weak focusing, strong focusing colliders and storage rings.
3- Accelerator devices and new acceleration techniques
Dipoles, quadrupoles and sextupoles, RF cavities.
4- Transverse beam dynamics in circular accelerators
Hamiltonian in Fernet-Serret coordinate system, Hill’s equation, transverse beam dynamics, matrix formalism, betatron function and tune, Courant-Snyder invariant and Twiss parameters.
5- Longitudinal beam dynamics in circular accelerators
Electromagnetic fields in RF devices, standing wave and travelling wave structures, momentum compaction, slippage factor and transition energy, synchrotron oscillations with small and large amplitude.
Prerequisites
Basic Physics and Basic electromagnetism courses
Books
Notes from the teacher
Material available on the web site
https://classroom.google.com/c/MTc3OTM0NDMxOTg0
Teaching mode
Lectures and visits
Frequency
Attendance is optional, but recommended. If a student has not been able to carry out laboratory experiments for some reason, recovery days are to be arranged with the teacher.
Exam mode
The final exam is oral and includes the defence of review of topics studied in the course.
Lesson mode
The course is based on traditional lectures in class, with some visits of didactic interest.
- Lesson code1042011
- Academic year2025/2026
- CourseElectronics Engineering
- CurriculumIngegneria Elettronica (percorso valido anche ai fini del conseguimento del doppio titolo italo-statunitense o italo-francese)
- Year2nd year
- Semester1st semester
- SSDFIS/01
- CFU6